There is only one 'attractive fixed point' in $\displaystyle x_{0}=3.5615528128 \dots$ and, because for any $\displaystyle x\ge -\frac{3}{2}$ is $\displaystyle |f(x)| < |x_{0}-x|$ , any $\displaystyle x_{1}\ge -\frac{3}{2}$ will produce a sequence that converges monotonically at $\displaystyle x=x_{0}$...